Plane trigonometry, by S.L. Loney.

SINES AND COSINES OF SMALL ANGLES. 333
In the series for sin 0 (Art. 280) let us omit the powers of 0 above the
third, and we have
0 -13 1349 1
0 ~1350 1350'
6 _ 1
6 1
1350 225 '
Hence 0=, so that the angle is I of a radian nearly.
If we desire a nearer approximation, we take the series for sin 0 and
omit powers above the 5th. We then have
03 05
- -Li3 5 = -1
60 1350'
120 20
This gives 4- 2002= -13 -25
Hence, by solving,
02= 10 1 J22480 150- 149.933312... _066688
15 15 15
100032
152
1-00016.. 0= radian.
15
This differs from the first approximation by about 6000th part.
60b0
Ex. 2. Solve approximately the equation
cos( +0 -49.
I
Since -49 is very nearly equal to, which is the value of cos 3, it
2 3
follows that 0 must be small.
The equation may be written
1 d3 1 1
cos — sin = (491)
1 cos10-^2/sin 0-49=-2 100.....................().
2 2 2 100. (1).
For a first approximation omit squares and higher powers of 0. By
Art. 280 this equation then becomes
1, 0 / 1
2 2 2 100'